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Dear Jorge,


Structural dynamics is just that, no matter what structure, be it a bridge or something altogether different. As I remember, the first time I had to resolve the problem of how to include a gap in a system was in 1975. It is coming back, now and then, like a 5-year tide.


Your total restraint at each end of the bridge is made up of soil, abutment, rubber pad and a gap.


  1. Both the pad and the gap are N/L elements. That means that if you insist on the spectrum response method, you have to develop an equivalent spring, representing all four elements.
  2. That linear spring is forcing-dependent, valid for a specific forcing or a specific response spectrum.
  3. The method of finding the equivalent k is a bit round-about, but quite rational.
  4. The reason for concern is when a method used makes the seismic effects smaller, than they really should be. With a rubber pad it can go either way, i.e. you can artificially increase or decrease the response.
  5. There is less doubt with a gap. If you choose to ignore it, for computational convenience, you are artificially increasing the natural frequency. This usually results in decreasing of the computed response, which is unconservative and unsafe.
  6. Unless the people who did those analyses know how to handle the two nonlinearities, the inclusion of only the linear stiffness component is unsafe.
  7. One of the ways to avoid creating equivalent springs is to conduct a time-dependent N/L simulation, but that is luxury for most engineering offices.
  8. If you wanted to see many examples of practical handling of nonlinearities, you could borrow from a library my first book, entitled “Dynamics of structures and machinery. Problems and solutions”, Wiley 1982.
  9. I am not in a position to comment on political and legal aspects of the situation.


Still, I believe that I confirmed your suspicion with regard to the quality of the results.